Method and apparatus to estimate channel tap

ABSTRACT

Briefly, a method an apparatus and a wireless communication device are provided. The wireless communication device includes a receiver to receive complex sequences of symbols. The receiver includes an estimator to estimate one or more channel taps. The estimator includes a memory to store at least a portion of one or more calculated values of an estimation matrix and is capable to estimate the one or more channel taps based on a stored portion of calculated values of the estimation matrix.

BACKGROUND OF THE INVENTION

Wireless communication systems such as, for example, cellularcommunication systems may include a plurality of modulation schemes. Themodulation schemes may be determined by a cellular standard which may bein use by the wireless communication system. An example of a cellularstandard may be Global System for Mobile Communications (GSM), GeneralPacket Radio Service (GPRS), Enhanced Data for GSM Evolution (EDGE) andthe like.

In EDGE/GSM modems and/or receivers, least squares (LS) channelestimation method may be used to estimate channel taps. The estimatedchannel taps may be used to estimate received symbols. For example, inthe LS channel estimation method, a pseudo-inverse matrix based on priorknown data such as, for example, training sequence symbols may be used.Furthermore, EDGE/GSM modems and/or receivers may include a digitalsignal processor (DSP). The DSP may load elements of a pseudo-inversematrix stored in a memory and may multiply received sequences of symbolsby the elements of the pseudo inverse matrix of the received sequences.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter regarded as the invention is particularly pointed outand distinctly claimed in the concluding portion of the specification.The invention, however, both as to organization and method of operation,together with objects, features and advantages thereof, may best beunderstood by reference to the following detailed description when readwith the accompanied drawings in which:

FIG. 1, is an illustration of a portion of a wireless communicationsystem according to an exemplary embodiment of the present invention;

FIG. 2, is an illustration of a block diagram of a mobile stationaccording to some exemplary embodiments of the present invention; and

FIG. 3, is an illustration of a flowchart of a method of estimating achannel tap scheme according to exemplary embodiments of the presentinvention.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity. Further, where consideredappropriate, reference numerals may be repeated among the figures toindicate corresponding or analogous elements.

DETAILED DESCRIPTION OF THE INVENTION

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of the invention.However it will be understood by those of ordinary skill in the art thatthe present invention may be practiced without these specific details.In other instances, well-known methods, procedures, components andcircuits have not been described in detail so as not to obscure thepresent invention.

Some portions of the detailed description, which follow, are presentedin terms of algorithms and symbolic representations of operations ondata bits or binary digital signals within a computer memory. Thesealgorithmic descriptions and representations may be the techniques usedby those skilled in the data processing arts to convey the substance oftheir work to others skilled in the art.

Unless specifically stated otherwise, as apparent from the followingdiscussions, it is appreciated that throughout the specificationdiscussions utilizing terms such as “processing,” “computing,”“calculating,” “determining,” or the like, refer to the action and/orprocesses of a computer or computing system, or similar electroniccomputing device, that manipulate and/or transform data represented asphysical, such as electronic, quantities within the computing system'sregisters and/or memories into other data similarly represented asphysical quantities within the computing system's memories, registers orother such information storage, transmission or display devices. Inaddition, the term “plurality” may be used throughout the specificationto describe two or more components, devices, elements, parameters andthe like. For example, “plurality of mobile stations” describes two ormore mobile stations.

It should be understood that the present invention may be used in avariety of applications. Although the present invention is not limitedin this respect, the circuits and techniques disclosed herein may beused in many apparatuses such as receivers of a radio system. Receiversintended to be included within the scope of the present inventioninclude, by way of example only, wireless local area network (WLAN)receivers, two-way radio receivers, digital system receivers, analogsystem receivers, cellular radiotelephone receivers and the like.

Types of cellular radiotelephone systems intended to be within the scopeof the present invention include, although are not limited to, CodeDivision Multiple Access (CDMA) and wideband CDMA (WCDMA) cellularradiotelephone portable devices for transmitting and receiving spreadspectrum signals, Global System for Mobile communication (GSM) cellularradiotelephone, Time Division Multiple Access (TDMA), Extended-TDMA(E-TDMA), GPRS, Extended GPRS, and the like.

Some embodiments of the invention may be implemented, for example, usinga machine-readable medium or article which may store an instruction or aset of instructions that, if executed by a machine (for example, bystations of wireless communication system, and/or by other suitablemachines), cause the machine to perform a method and/or operations inaccordance with embodiments of the invention. Such machine may include,for example, any suitable processing platform, computing platform,computing device, processing device, computing system, processingsystem, computer, processor, or the like, and may be implemented usingany suitable combination of hardware and/or software. Themachine-readable medium or article may include, for example, anysuitable type of memory unit, memory device, memory article, memorymedium, storage device, storage article, storage medium and/or storageunit, for example, memory, removable or non-removable media, erasable ornon-erasable media, writeable or re-writeable media, digital or analogmedia, hard disk, floppy disk, Compact Disk Read Only Memory (CD-ROM),Compact Disk Recordable (CD-R), Compact Disk Rewriteable (CD-RW),optical disk, magnetic media, various types of Digital Versatile Disks(DVDs), a tape, a cassette, or the like. The instructions may includeany suitable type of code, for example, source code, compiled code,interpreted code, executable code, static code, dynamic code, or thelike, and may be implemented using any suitable high-level, low-level,object-oriented, visual, compiled and/or interpreted programminglanguage, e.g., C, C++, Java, BASIC, Pascal, Fortran, Cobol, assemblylanguage, machine code, or the like.

Turning to FIG. 1, a wireless communication system such as, for example,a cellular communication system 100 in accordance with exemplaryembodiment of the invention, is shown. Although the scope of the presentinvention is not limited in this respect, cellular system 100 mayinclude a base station 110, a mobile station 120, an uplink 130 and adownlink 140. Uplink 130 and downlink 140 may include one or morechannels. In accordance with embodiments of the invention, a channel maybe depicted as a physical transfer medium that may be used to transfersignals. Furthermore, a channel may be a combination of the physicaltransfer medium, components of the transmitter and/or receiver and mayinclude channel taps (for example, symbols). According to embodiments ofthe invention, the channel may be estimated and/or measured by a channeltime span. In embodiments of the invention, the channel time span maynot exceed a certain number of symbols, for example seven symbols. Inaddition , the channel time span may not exceed a predetermined delayspread, if desired.

Although the scope of the present invention is not limited in thisrespect, mobile station 120 may include a modem 125, for example a GPRS,EDGE or the like. According to at least one embodiment of the invention,modem 125 may be used to estimate the channel taps according to apre-stored portion of calculation of an estimation matrix.

Turning to FIG. 2, a block diagram of a mobile station 200, according toan exemplary embodiment of the invention is shown. Although the scope ofthe present invention is not limited in this respect, mobile station 200may include an antenna 210 and a receiver 220 which may include, forexample, a modem such as, for example, GPRS modem, EDGE modem or thelike. In embodiments of the invention, receiver and/or modem 220 mayinclude an estimator 230. Estimator 230 may include the followingsoftware and/or hardware components and/or signals, if desired. In thisexemplary embodiment, estimator 230 may include a memory 240, multiplier275, sequences of complex symbols 250, 255, a real sequence generator260, calculators 265, 270, a constant phase 280, a parameter L 263, acomplex received symbols 285, rotators 277, 287, and a channel tap 290.According to this exemplary embodiment, memory 240 may store at least aportion of a calculation of estimation matrix 245. According toembodiments of the invention, parameter L 263 may include the number ofchannel taps to be estimated, if desired.

Although the scope of the present invention is not limited in thisrespect, estimator 230 may be capable of performing a least squares (LS)algorithm to estimate channel tap 290. For example, LS algorithm maycalculate a set of complex pseudo-inverse matrix depending on atransmitted training sequence and a number of parameters to beestimated. For example, the parameters may include a training sequencecode number, a channel length, a modulation type or the like. Accordingto one or more embodiments of the invention, the pseudo-inverse matrixmay be depicted by the following equation:PseudoInvMat=(S ^(H) S)⁻¹ S ^(H)   (Equation 1)where S^(H) may be a convolution matrix such as, for example, atranspose Toeplitz matrix, which may be built from known trainingsymbols. For example, a size of S^(H) may be L×(M−L+1) of complexelements, wherein M may be the training sequence length and L may be thenumber of parameters to be estimated, e.g., parameter L 263. Forexample, convolution matrix S^(H) may include X_(n) sequences oftransmitted training symbols, and convolution matrix S^(H) may bedepicted as follows: $\begin{matrix}{S^{H} = \begin{pmatrix}x_{i} & x_{i - 1} & \ldots & x_{i - {({L - 1})}} \\x_{i + 1} & \quad & \ldots & x_{i + 2 - L} \\\vdots & \vdots & ⋰ & \vdots \\x_{i + N - 1} & x_{i + N - 2} & \ldots & x_{i + N - L}\end{pmatrix}} & \left( {{Equation}\quad 2} \right)\end{matrix}$

Where i=L−1 and N=M−L+1

Although the scope of the present invention is not limited in thisrespect, estimator 230 may estimate channel tap 290 by multiplyingPseudoInvMat (Equation 1) with the received signal r(n) to produce avector of estimated channel taps, e.g. EstChTaps(m), as depicted by thefollowing equation: $\begin{matrix}{{{{EstChTaps}(m)} = {\sum\limits_{n = 0}^{M - L + 1}{{{PseudoInvMat}\left( {m,n} \right)}^{*}{r(n)}}}},{m = {{0\text{:}\quad L} - 1.}}} & \left( {{Equation}\quad 3} \right)\end{matrix}$

Where r(n) may be the received signal at time n; and

EstChTaps(m) is the estimated channel taps at time m.

Although the scope of the present invention is not limited in thisrespect, according to one embodiment of the invention, memory 240 maystore a portion of calculations of estimation matrix 245. For example,portion of estimation matrix 245 may be InvMat=(S^(H)S)⁻¹ and theestimation matrix may be PseudoInvMat=(S^(H)S)⁻¹S^(H) in accordance withEquation 1. For example, in one embodiment of the invention, S^(H) maybe a transpose Toeplitz matrix, which may be constructed from apredetermined complex sequence of symbols 250. Real sequence generator260 may convert S^(H) to real sequences, if desired Calculator 265 maycalculate a portion of the estimation matrix 245 (e.g.InvMat=(S^(H)S)⁻¹) from the predetermined complex sequence of symbols250.

Although the scope of the present invention is not limited in thisrespect, receiver 220 may receive a burst of symbols. Calculator 270 maymultiply InvMat=(S^(H)S)⁻¹ with a portion of estimation matrix 245 e.g.S^(H) in order to produce the desired pseudo-inverse matrix, e.g.,PseudoInvMat=InvMat·S^(H)

In some embodiments of the invention, for example, matrix InvMat may beconjugated symmetric or real symmetric around a main diagonal of thematrix InvMat. Thus, only a portion of the matrix, for example, a halfmatrix, may be stored in memory 240. Furthermore, the dimension of thestored portion of the matrix may be (L+1)×L/2 elements.

Although the scope of the present invention is not limited in thisrespect, the received signal r at time n may be depicted by: (canceljustification) $\begin{matrix}{{{r(n)} = {{\sum\limits_{k}{{h(k)}{X\left( {n - k} \right)}}} + {N(n)}}},{n = {L\quad\ldots\quad M}},{k = {{0\quad\ldots\quad L} - 1}}} & \left( {{Equation}\quad 4} \right)\end{matrix}$

Wherein:

-   -   h(k) may be the channel taps at time k;    -   X(n-k) may the transmitted training sequence at time n-k; and    -   N_(n) may be the noise at time n.

According to other embodiments of the invention, receiver 220 may be aGPRS and/or EDGE modem. In this embodiment, receiver 220 may receiveGaussian Minimum Shift Keying (GMSK) and/or 8 phase Shift Keying (8PSK)training symbols, e.g. complex sequences 250, 255. Real sequencegenerator 260 may rotate the symbols of the complex sequences 250, 255by a linear phase θn, for example, constant phase 280, to generate areal matrix. For example, complex sequences 250 and 255 may include 8PSKand/or GMSK sequences. For 8PSK sequence the phase θ may be$\theta = {{\theta 1} = \frac{3\pi}{8}}$and for GMSK the phase θ may be$\theta = {{\theta 2} = {\frac{\pi}{2}.}}$In addition, complex sequences of symbols 250, 255 may include aconstant predetermined phase difference. For example, in someembodiments of the invention, the predetermined phase difference between8PSK training symbols and GMSK training symbols may be $\frac{\Pi}{8},$if desired. Additionally or alternatively, it should be understood thatin embodiments of the present invention, any number of complex sequenceswhich include a linear phase difference may be used.

According to this embodiment of the invention, calculator 265 maygenerate a portion of a real estimation matrix based on the real matrix,if desired The portion of the real estimation matrix (e.g. estimationmatrix 245) may be stored in memory 240.

Although the scope of the present invention is not limited to thisrespect, calculator 265 may convert the real matrix to a portion ofestimation matrix (e.g. InvMat=(S^(H)S)⁻¹⁾ by performing calculationsaccording to the following equation:X′(n)=e ^(jθn) X(n)   (Equation 5)

wherein:

-   -   X′(n), n=0:25, may be a real de-rotated transmitted training        sequence symbols which may be provided by real sequence        generator 260; and    -   X(n) may be the transmitted training sequence complex rotated        symbols.        Furthermore, Calculator 265 may generate the matrix S^(H) based        on X′(n) (e.g. a real matrix) to provide an InvMat=(S′^(H)S′)⁻¹        and calculator 270 may calculate PseudoInvMat=InvMat·S^(H), if        desired.

Although the scope of the present invention is not limited in thisrespect, more than one real and/or complex matrix, e.g., a portion ofestimation matrix 245, for example, InvMat=(S′^(H)S′)¹, may be stored inmemory 240 and may depend on parameter L 263, sequences 250, 255, themodulation type, and the constant phase 280, if desired.

Although the scope of the present invention is not limited in thisrespect, the received signal r(n) may be depicted by:${r(n)} = {{\sum\limits_{k}{{h(k)}{X\left( {n - k} \right)}{\mathbb{e}}^{- {{j0}{({n - k})}}}}} + {{N(m)}.}}$Rotator 287 may rotate the receive signal and may output the signalaccording to the following equation:r′(n)=r(n)*e ^(jθn) , n=L: M   (Equation 6)The result output signal r′(n) may thus be: $\begin{matrix}{{{r(n)}{\mathbb{e}}^{{j\theta}\quad n}} = {{\sum\limits_{k}{\left( {{h(k)}{\mathbb{e}}^{{j\theta}\quad k}} \right){X\left( {n - k} \right)}}} + {{N(n)}{\mathbb{e}}^{{j\theta}\quad n}}}} & \left( {{Equation}\quad 7} \right)\end{matrix}$and multiplier 275 may estimate channel tap 290 based on the storedportion of the estimation matrix 245. For example, the estimation ofchannel taps 290 may be performed by calculating h(m) according to thefollowing equation: $\begin{matrix}{{{h(m)} = {\sum\limits_{n = 0}^{M - L + 1}{{{PseudoInvMat}\left( {m,n} \right)}^{*}{r(n)}}}},{m = {{0\text{:}\quad L} - 1}}} & \left( {{Equation}\quad 8} \right)\end{matrix}$The estimated channel taps may be produced by rotating h(m). Accordingto this embodiment of the invention, rotator 277 may rotate h(m) toproduce channel tap 290 as depicted by the following equation:EstChTaps(m)=h(m)e ^(−jθm) , m=0:1: L   (Equation 9).

Although the scope of the present invention is not limited in thisrespect, it should be understood that the blocks and/or components ofreceiver 220 are shown as example only and may be implemented byhardware and/or by software and/or by any combination of hardware andsoftware such as, for example a digital signal processor, if desire.

Turning to FIG. 3, a flowchart of a method to estimate a channel tapaccording to exemplary embodiments of the present invention is shown.Although the scope of the present invention is not limited to thisrespect, according to some exemplary embodiments of the invention, GMSKcomplex sequence (text block 300) and 8PSK complex sequence (text box310) may be provided to a real sequence generator (e.g. real sequencegenerator 260). Real sequence generator may generate a real sequence byrotating the symbols of GMSK complex sequence (text block 300) and 8PSKcomplex sequence (text box 310) by a constant phase θ, respectively(text block 320).

Although the scope of the present invention is not limited in thisrespect, a real estimation matrix (S) may be generated from the realsequence (text block 330) and at least a portion of the real estimationmatrix, for example (S^(H)S)⁻¹ may be stored in a memory (text block340). According to embodiments of the invention, estimation of one ormore channel taps may be done by multiplying the stored portion of thereal estimation matrix (S^(H)S)⁻¹ by a matrix S^(H) and multiplying theresult by the rotated received symbols r′(n)=r(n)*e^(jθn), if desired(text block 350).

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those skilled in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the invention.

1. A method comprising: storing at least a portion of one or morecalculated values of an estimation matrix; and estimating a channel tapbased on a received sequence of symbols and the stored portion of thecalculated values of the estimation matrix.
 2. The method of claim 1,comprising: calculating the portion of the estimation matrix from apredetermined complex sequence of symbols.
 3. The method of claim 1,comprising: calculating the portion of the estimation matrix from apredetermined real sequence of symbols.
 4. The method of claim 1,further comprising: generating a real sequence of symbols from a firstand second predetermined complex sequences of symbols; generating a realestimation matrix based on the real sequence of symbols; storing aportion of the real estimation matrix; and estimating the channel tapbased on the stored portion of the real estimation matrix.
 5. The methodof claim 4, comprising: providing a constant predetermined phasedifference between the first and second predetermined complex sequencesof symbols.
 6. The method of claim 1, comprising: generating a realsequence of symbols based on a predetermined complex sequence ofsymbols. generating a real estimation matrix based on the real sequenceof symbols; storing a portion of the real estimation matrix; andestimating the channel tap based on the stored portion of the realestimation matrix.
 7. An apparatus comprising: a receiver to receive asequence of symbols; a memory to store at least a portion of one or morecalculated values of an estimation matrix; and a estimator to estimate achannel tap based on the stored portion of the estimation matrix.
 8. Theapparatus of claim 7, further comprising: a first calculator tocalculate the portion of the estimation matrix from a predeterminedcomplex sequence of symbols; and a second calculator to calculate theestimation matrix based on at least the portion of the estimationmatrix.
 9. The apparatus of claim 8, comprising: a real sequencegenerator to convert the predetermined complex sequence of symbols intoa real sequence of symbols, wherein the first calculator is able tocalculate at least the portion of the estimation matrix from the realsequence of symbols
 10. The apparatus of claim 7, further comprising: areal sequences generator to generate a real sequence of symbols based ona first and second predetermined complex sequences of symbols; and acalculator to generate a real estimation matrix based on the realsequence of symbols.
 11. The apparatus of claim 10, wherein the memoryis able to store a portion of the real estimation matrix.
 12. Theapparatus of claim 10, wherein the estimator is able to estimate thechannel tap based on the stored portion of the real estimation matrix.13. The apparatus of claim 10, comprising: a constant predeterminedphase difference between the first and second predetermined complexsequences of symbols.
 14. A wireless communication device comprising: areceiver having a memory to store at least a portion of one or morecalculated values of an estimation matrix; and an estimator to estimatea channel tap based on the stored portion of the estimation matrix. 15.The wireless communication device of claim 14, wherein the receiverfurther comprises: a first calculator to calculate the portion of theestimation matrix from a predetermined complex sequence of symbols; asecond calculator to calculate the estimation matrix based on at leastthe portion of the estimation matrix; and a rotator to rotate receivedsymbols by a constant phase.
 16. The wireless communication device ofclaim 14, wherein the receiver comprises: a real sequence generator toconvert the predetermined complex sequence of symbols to a real sequenceof symbols, wherein the first calculator is able to calculate at leastthe portion of the estimation matrix from the real sequence of symbols.17. The wireless communication device of claim 14, wherein the receiverfurther comprises: a real sequences generator to generate a realsequence of symbols based on a first and second predetermined complexsequences of symbols; and a calculator to generate a real estimationmatrix based on the real sequence of symbols.
 18. The wirelesscommunication device of claim 17, wherein the memory is able to store aportion of the real estimation matrix.
 19. The wireless communicationdevice of claim 17, wherein the estimator is able to estimate thechannel tap based on the stored portion of the real estimation matrix.20. The wireless communication device of claim 17, wherein the receivercomprises: a constant predetermined phase difference between the firstand second predetermined complex sequences of symbols.
 21. The wirelesscommunication device of claim 17, wherein the receiver is able to theestimate the channel tap based on the complex sequences of symbols of anEnhanced Data for Global system for mobile communications Evolution(EDGE) standard.
 22. The wireless communication device of claim 17,wherein the receiver is able to estimate the channel tap base on complexsequences of symbols of a general packet radio service standard.
 23. Awireless communication device comprising: a dipole antenna operablycoupled to a receiver having a memory to store at least a portion of oneor more calculated values of an estimation matrix; and an estimator toestimate a channel tap based on the stored portion of the estimationmatrix.
 24. The wireless communication device of claim 23, wherein thereceiver further comprises: a first calculator to calculate the portionof the estimation matrix from a predetermined complex sequence ofsymbols; and a second calculator to calculate the estimation matrixbased on the portion of the estimation matrix.
 25. The wirelesscommunication device of claim 23, wherein the receiver comprises: a realsequence generator to convert the predetermined complex sequence ofsymbols to a real sequence of symbols, wherein the first calculator isable to calculate the portion of the estimation matrix from the realsequence of symbols.
 26. The wireless communication device of claim 23,wherein the receiver comprises: a real sequences generator to generate areal sequence of symbols from a first and second predetermined complexsequences of symbols; and a calculator to generate a real estimationmatrix based on the real sequence.
 27. The wireless communication deviceof claim 26, wherein the memory is able to store a portion of the realestimation matrix.
 28. The wireless communication device of claim 26,wherein the estimator is able to estimate the channel tap based on thestored portion of the real estimation matrix.
 29. The wirelesscommunication device of claim 26, wherein the receiver comprises: aconstant predetermined phase difference between the first and secondpredetermined complex sequences of symbols.
 30. The wirelesscommunication device of claim 26, wherein the receiver is able to theestimate the channel tap based on the complex sequences of symbols of anEnhanced Data for Global system for mobile communications Evolution(EDGE) standard.
 31. The wireless communication device of claim 26,wherein the receiver is able to estimate the channel tap base on complexsequences of symbols of a general packet radio service standard.
 32. Awireless communication system comprising: a wireless communicationdevice having a receiver to receive complex sequences of symbols, amemory to store at least a portion of one or more calculated values ofan estimation matrix and an estimator to estimate a channel tap based onthe stored portion of the estimation matrix.
 33. The wirelesscommunication system of claim 32, wherein the estimator comprises: afirst calculator to calculate the portion of the estimation matrix froma predetermined complex sequence of symbols; and a second calculator tocalculate the estimation matrix based on the portion of the estimationmatrix.
 34. The wireless communication system of claim 32, wherein theestimator comprises: a real sequence generator to convert thepredetermined complex sequence of symbols to a real sequence of symbols,wherein the first calculator is able to calculate the portion of theestimation matrix from the real sequence of symbols.
 35. The wirelesscommunication system of claim 32, wherein the estimator comprises: areal sequences generator to generate a real sequence of symbols from afirst and second predetermined complex sequences of symbols; and acalculator to generate a real estimation matrix based on the realsequence.
 36. The wireless communication system of claim 35, wherein theestimator comprises: a constant predetermined phase difference betweenthe first and second predetermined complex sequences of symbols.
 37. Anarticle comprising a storage medium having stored thereon instructionsthat, when executed, result in: storing at least a portion of one ormore calculated values of an estimation matrix; and estimating a channeltap based on a received sequence of symbols and the stored portion ofthe calculated values of the estimation matrix.
 38. The article of claim37, wherein the instructions, when executed, result in: calculating theportion of the estimation matrix from a predetermined complex sequenceof symbols.
 39. The article of claim 37, wherein the instructions, whenexecuted, result in: calculating the portion of the estimation matrixfrom a predetermined real sequence of symbols.
 40. The article of claim37, wherein the instructions, when executed, result in: generating areal sequence of symbols from a first and second predetermined complexsequences of symbol; generating from the real sequence a real estimationmatrix; storing a portion of the real estimation matrix; and estimatinga channel tap based on the stored portion of the real estimation matrix.41. The article of claim 37, wherein the instructions, when executed,result in: generating a real sequence of symbols from a predeterminedcomplex sequence of symbols; generating from the real sequence a realestimation matrix; storing a portion of the real estimation matrix; andestimating a channel tap based on the stored portion of the realestimation matrix.